# Present value of uniform gradient series

## Input(s)

\(i_{e}\): Effective Interest or Discount Rate (fraction)

\(\mathrm{t}\): Time (year)

G: Annual Change (Positive or Negative) (currency unit)

\(A_{1}\): Cash Flow at the End of the First Year (currency unit)

## Output(s)

\(A_{v}\): Present Value of Uniform Gradient Series (currency unit)

## Formula(s)

\[
A_{v}=A_{1} \pm G *\left(\frac{1}{i_{e}}-\frac{t}{\left(\left(1+i_{e}\right)^{t}\right)-1}\right)
\]

## Reference(s)

Mian, M. A. 2011. Project Economics and Decision Analysis Volume 1: Deterministic Models, Second Edition. Tulsa, Oklahoma: PennWell Corporation. Chapter 2, Page: 68.